$B$ is the midpoint of $\overline{AC}$ $A$ $B$ $C$ If: $ AB = 4x - 7$ and $ BC = 2x + 5$ Find $AC$.
A midpoint divides a segment into two segments with equal lengths. ${AB} = {BC}$ Substitute in the expressions that were given for each length: $ {4x - 7} = {2x + 5}$ Solve for $x$ $ 2x = 12$ $ x = 6$ Substitute $6$ for $x$ in the expressions that were given for $AB$ and $BC$ $ AB = 4({6}) - 7$ $ BC = 2({6}) + 5$ $ AB = 24 - 7$ $ BC = 12 + 5$ $ AB = 17$ $ BC = 17$ To find the length $AC$ , add the lengths ${AB}$ and ${BC}$ $ AC = {AB} + {BC}$ $ AC = {17} + {17}$ $ AC = 34$